ON THE EMPTY BALLS OF A CRITICAL OR SUBCRITICAL BRANCHING RANDOM WALK

Let{Z_(n)}_(n)≥0 be a critical or subcritical d-dimensional branching random walk started from a Poisson random measure whose intensity measure is the Lebesugue measure onℝ^(d).Denote by R_(n):=sup{u>0:Z_(n)({x∈ℝ^(d):∣x∣<u})=0}the radius of the largest empty ball centered at the origin of Zn.In this work,we prove that after suitable renormalization,Rn converges in law to some non-degenerate distribution as n→∈.Furthermore,our work shows that the renormalization scales depend on the offspring law and the dimension of the branching random walk.This completes the results of Révész[13]for the critical binary branching Wiener process.

Preparation and Properties of Spray Polyurea Elastomer for Aquaculture Foam Floating Balls

[Objectives] This study was conducted to develop a polyurea elastomer which can be sprayed on the surface of expanded polystyrene (EPS) floating balls, so as to improve the surface strength and service life of the floating balls. [Methods] The effects of the types and amounts of isocyanate, chain extenders and polyether polyols on the gelation rate, adhesion and wear resistance of polyurea elastomer were investigated, and it was finally determined the preparation process of polyurea elastomer using liquid isophorone diisocyanate (IPDI) and amino-terminated polyether (D2000) as the main raw materials, dimethylthiotoluene diamine (E300) as the chain extender and silica as the wear resistance modifier through two-step solution polymerization of prepolymerization and chain extension. [Results] The physical properties and chemical resistance tests of spray polyurea elastomer showed that it had good physical properties and acid and alkali resistance, and could meet the requirements of spraying and protection of EPS floating ball surface in marine environment. [Conclusions] Polyurea elastomer coating can improve the aging resistance, wear resistance and acid and alkali resistance of EPS floating balls, and prevent them from being fragile and floating randomly to form marine floating garbage which results in "white pollution".

Existence of a Hölder Continuous Extension on Embedded Balls of the 3-Torus for the Periodic Navier Stokes Equations

This article gives a general model using specific periodic special functions, which is degenerate elliptic Weierstrass P functions whose presence in the governing equations through the forcing terms simplify the periodic Navier Stokes equations (PNS) at the centers of cells of the 3-Torus. Satisfying a divergence-free vector field and periodic boundary conditions respectively with a general spatio-temporal forcing term which is smooth and spatially periodic, the existence of solutions which have finite time singularities can occur starting with the first derivative and higher with respect to time. The existence of a subspace of the solution space where v3 is continuous and {C, y1, y12}, is linearly independent in the additive argument of the solution in terms of the Lambert W function, (y12=y2, C∈R) together with the condition v2=-2y1v1. On this subspace, the Biot Savart Law holds exactly [see Section 2 (Equation (13))]. Also on this subspace, an expression X (part of PNS equations) vanishes which contains all the expressions in derivatives of v1 and v2 and the forcing terms in the plane which are related as with the cancellation of all such terms in governing PDE. The y3 component forcing term is arbitrarily small in ε ball where Weierstrass P functions touch the center of the ball both for inviscid and viscous cases. As a result, a significant simplification occurs with a v3 only governing PDE resulting. With viscosity present as v changes from zero to the fully viscous case at v =1 the solution for v3 reaches a peak in the third component y3. Consequently, there exists a dipole which is not centered at the center of the cell of the Lattice. Hence since the dipole by definition has an equal in magnitude positive and negative peak in y3, then the dipole Riemann cut-off surface is covered by a closed surface which is the sphere and where a given cell of dimensions [-1, 1]3 is circumscribed on a sphere of radius 1. For such a closed surface containing a dipole it necessarily follows that the flux at the surface of the sphere of v3 wrt to surface normal n is zero including at the points where the surface of sphere touches the cube walls. At the finite time singularity on the sphere a rotation boundary condition is deduced. It is shown that v3 is spatially finite on the Riemann Sphere and the forcing is oscillatory in y3 component if the velocity v3 is. It is true that . A boundary condition on the sphere shows the rotation of a sphere of viscous fluid. Finally on the sphere a solution for v3 is obtained which is proven to be Hölder continuous and it is shown that it is possible to extend Hölder continuity on the sphere uniquely to all of the interior of the ball.

Water Extract of Rice False Smut Balls Activates Nrf2/HO-1 and Apoptosis Pathways,Causing Liver Injury

Ustiloxins are vital cyclopeptide mycotoxins originally isolated from rice false smut balls that form in rice spikelets infected by the fungal pathogen Ustilaginoidea virens.The toxicity of the water extract of rice false smut balls(RBWE) remains to be investigated.Studies have shown that RBWE may be toxic to animals,but toxicological evidence is still lacking.In this study,we found that the IC50 values of RBWE to BNL CL.2 cells at 24 and 48 h were 40.02 and 30.11 μg/m L,respectively,with positive correlations with dose toxicity and time toxicity.After treatment with RBWE,the number of BNL CL.2 cells decreased significantly,and the morphology of BNL CL.2 cells showed atrophy and wall detachment.RBWE induced DNA presynthesis phase arrest of BNL CL.2 cells,increased the proportion of apoptotic cells and inhibited cell proliferation.RBWE up-regulated reactive oxygen species(ROS) levels and lowered mitochondrial membrane potentials.Additionally,Western blot and q RT-PCR results suggested that RBWE exerted the above effects by promoting the Nrf2/HO-1 and caspase-induced apoptosis pathways in vitro and in vivo.The contents of alanine aminotransferase,aspartate aminotransferase,alkaline phosphatase,and total bile acids in the serum of mice from Institute of Cancer were significantly up-regulated by RBWE.At the same time,RBWE can lead to increases in ROS and malondialdehyde contents,decreases in contents of oxidized glutathione,glutathione and reduced glutathione,as well as decrease in catalase and superoxide dismutase activities in mouse liver tissues,demonstrating that oxidative stress occurred in mice.Moreover,liver damage was further detected by haematoxylin-eosin staining and electron microscopy to verify the damage to the mice caused by RBWE.In general,RBWE may cause hepatotoxicity in vivo and in vitro via the apoptosis pathway,which provides a reference for hepatotoxicity and its mechanism of action.

Balls into bins分配器算法

针对传统的bitmap分配器算法中没有反馈机制,导致搜索不能很好地适应各种情况的问题。分析得到bitmap分配器算法中空闲块的搜索问题实际上是一个负载平衡的问题,因此将ballsintobins的负载平衡问题的研究结果应用在bitmap分配器上。将bitmap分成不同的区,从中选出负载量小的区进行分析,经对比分析和对C3I系统的实际检验表明,这种分配器算法的确优于传统的bitmap分配器算法。

Effects of austempering temperature on microstructure and surface residual stress of carbidic austempered ductile iron(CADI) grinding balls

The effects of austempering temperature on microstructure and surface residual stress of carbidic austempered ductile iron （CADI） grinding balls were systematically investigated in this work. The microstructures were oberserved by optical metallography and analyized by X-ray diffraction. The surface residual stress measured by the cutting method is mainly composed of thermal stress and phase transformation stress.The thermal stress in grinding balls was determined by ANSYS simulation technique, and the surface phase transformation stress was obtained by subtracting the simulated surface thermal stress from the measured surface residual stress. Results show that all microstructures consist of ausferrite, white-bright zones （mixture of martensite and austenite）, nodular graphite, and carbides. The distribution of ausferrite shows uniform. With the increase of austempering temperature, the volume fraction and carbon content of austenite increase, whereas the amount of white-bright zone decreases. In addition, the surface residual stress increases with the increase of austempering temperature. Only the tension exists at the austempering temperature of 200 ℃, and the pressure exists at the austempering temperature of 220-260 °C. The thermal stress changes from the tension on the inside with the radius of 0-35 mm to the pressure on the outside with the radius of 35-62.5 mm, and the stress balance state presents at the radius of 35 mm. It is also found that the transformation stress is related to the content of carbon-rich austenite, and will reduce by 5.03 MPa accompanied with 1vol.% increase of the austenite.The thermal compressive stress and the transformation tensile stress on the surface both decrease with the increase of the austempering temperature.

Anatomical Structures of " Lepidodendron " pulchrum Zhang in Coal-balls from the Taiyuan Formation (Lower Lower Permian) in Shandong Province, North China

This study reports the anatomical structures of a kind of lepidodendralean stem in coal balls from the early Early Permian Taiyuan Formation in Yanzhou Mining District, southwestern Shandong Province, North China. The leaf cushion is slightly rhomboid in outline with a height of 9 - 10 mm and a width of 7.5 9.0 mm and its lower sides are slightly longer than the upper ones. The top and basic angles of the leaf cushion are truncate and the basic angle is slightly elongate. The upper part of the leaf cushion is strongly high-rising. The leaf sear is large and lenticular in shape. The leaf trace is wide and V-shaped in the leaf scar, and horizontally elongate within the leaf cushion. The leaf trace and lateral parichnos strand extend at a nearly horizontal course outward within the leaf cushion. The ligular pit is deep and extends outward at an oblique course and its aperture is located near the top angle of the leaf scar. No infrafoliar parichnos strands are present. The stem is probably siphonostelic and its pith is probably parenchymatous. The primary xylem is exarch with a nearly smooth outer margin. Only the outer cortex is present and it consists of alternately-arranged radial cell bands and gaps within which the are-shaped or V-shaped leaf traces can be seen. The concave side of the leaf trace is toward the center of the stem. No bundle sheath is developed. Periderm is well-developed and consists of phelloderm and phellem in nearly equal thickness. Compared with the lepidodendralean stems of the Cathaysian and Euramerican Floras, the present specimens are most close to an impression-compression species Lepidodendron pulchrum Zhang in morphology of the leaf cushion and they are put into this species temporarily. Whether the present specimens or the type specimens of L. pulchrum are very different from Lepidodendron Sternburg sensu DiMichele, thus the correct nomenclature and classification of L. pulchrum needs to be reconsidered based on the study of better- and anatomically-preserved stems and fertile organs in the future. Because 'L'. pulchrum possesses the mixed features of several genera of Euramerican lepidodendralean stems, it bears significance to study the origin and evolution of the Cathaysian lepidodendralean lycopods.

LINEAR SINGULAR INTEGRAL EQUATION ON DOMAINS COMPOSED BY BALLS

For domains composed by balls in C^n, this paper studies the boundary behaviour of Cauchy type integrals with discrete holomorphic kernels and the corresponding linear singular integral equation on each piece of smooth lower dimensional edges on the boundary of the domain.

Maillard reaction in Chinese household-prepared stewed pork balls with brown sauce:potentially risky and volatile products

The stewed pork balls with brown sauce(SPB-BS)in China is well known for its delicacy and preferred by consumers.Maillard reaction(MR)is widespread in SPB-BS due to the use of sugar,meat and sauce in the thermal process.However,there is a lack of research on its risk and flavor by MR.By solid phase extraction combined with HPLC-MS,4 kinds of harmful compounds including acrylamide(AA),heterocyclic aromatic amines(HAAs),4-methylimidazole(4-MEI)and furan were analyzed in SPB-BS and their amounts ranged 0.05–0.50 mg/kg.The quantitative formula was proposed to evaluate the risk value of the SPB-BS,after taking into account the content,acceptable daily intake(ADI)and carcinogenicity of each compound.The risk values were in range of 0.57–37.93,suggesting that the risk caused by MR in SPB-BS was low.By head space-solid phase microextraction combined with GC-MS,57 volatile compounds in SPB-BS were identified with the dominant contribution of alcohols,aldehydes,acids and esters.Based on the structures of these compounds and the composition of SPB-BS,lipid oxidation and MR are inferred to be responsible for the formation of the harmful and volatile compounds.In addition,the added sauces and oil provides the main precursors to form the harmful and volatile compounds in SPB-BS,so it is necessary to point out a balance between them in the further study.

Anatomically-preserved Lepidodendralean Plants from Permian Coal Balls of China: Sigillariopsis Scott

Three kinds of anatomically_preserved lepidodendralean leaves from Permian coal balls of China were studied. They all have double xylem strands, which is consistent with the genus Sigillariopsis Scott. Compared with the species of Sigillariopsis , they are considered as three new species: S. shanxiensis sp. nov. and S. taiyuanensis sp. nov. from Coal Seam 7 in the upper part of the Taiyuan Formation (lower Lower Permian), Xishan Coal Field, Taiyuan, Shanxi Province and S. guizhouensis sp. nov. from Coal Seam 1 in the Wangjiazhai Formation (upper Upper Permian), Shuicheng Coal Mining District, Guizhou Province. Based on the associated organs of lepidodendraleans other than leaves and the information of the Euramerican lepidodendraleans, the affinities of the three new species of Sigillariopsis are discussed and they are probably leaves of Sigillaria Brongniart. In Euramerican Flora, Sigillaria (including its leaves Sigillariopsis ) mainly lived in the Carboniferous period and in the Cathaysian Flora they lived in the Upper Carboniferous to upper Upper Permian periods in rare localities. The leaves and fertile organs of Sigillaria have not been reported from the Cathaysian Flora to date. Three new species of the Permian anatomically_preserved leaves of Sigillaria not only increase the diversity of the Cathaysian sigillarian but also bear important significance on the evolution of sigillarian plants and the relationship of the Cathaysian and Euramerican lepidodendraleans.

A New Shaping Model for Green Ceramic Balls

The shaping quality of green ceramic balls is directly related to the efficiency and cost of later machining for the ceramic balls. Until now the shaping for green ceramic balls is still conducted by handwork. In this paper, a new shaping model for green ceramic balls was designed. In the new model, two grinding wheels with the same generator line as circular arc are mounted on symmetry, and their axes are parallel. The green ball can be put in the enveloping space formed by the two grinding wheels. The radius of generator line must be equal to or slightly greater than the final radius of the green balls, which can ensure that an ideal sphere can be enveloped by the generator of grinding wheel as grinding the green body surface with the wheels. One of the two wheels rotates in upward direction at high speed v 1, conversely, the other wheel rotates in downward direction at low speed v 2, and a cluster of compressed air is exerted on the green ball above for canceling out the force acting upon the green ball created by the action of the grinding wheel revolving at high speed and avoiding that the green ball jumps off its station. Because of the randomness of the distributions of abrasive grains on the surface of grinding wheels, the size and shape of the abrasive grains, and the posture of green body when falling into the grinding space, the values and directions of the resultant forces and torques exerted on the body, caused by the tow wheels, are random, the rotation of green body is irregular under the actions of the compressed air and the wheels. The irregularity of rotation can ensure an ideal sphere in theory. Experiment researches indicate that the new shaping model can improve the spherical deviations and the size distribution of the green ceramic balls, raise the production, and reduce the costs. The spherical deviations can be improved to 0.04 mm easily. It can be observed by SEM that there is no crack in the surface of sintered ceramic balls shaped with the new model in green blank.

Experimental Research on Residual Stress in Surface of Silicon Nitride Ceramic Balls

The influence of the residual stress in surface of ceramic balls on the fatigue life is large, because the life of silicon nitride ball bearings is more sensitive to the load acted on the bearings than the life of all-steel ball bearings. In this paper, the influence of thermal stress produced in sintering and mechanical stress formed in lapping process on residual stress in surface of silicon nitride ceramic balls was discussed. The residual compress stress will be formed in the surface of silicon nitride ceramic balls after sintering. The residual tensile stress will be formed in surface of silicon nitride ceramic balls in lapping process, and the size of abrasive particle is smaller, such trend is stronger. In this paper the residual stress was measured by the xylometric measurement in which the material in surface was peeled with lapping. The distribution of residual stress in surface can be calculated with the variation in specific volume. The technological parameter with which the material was peeled by lapping was given, for minimizing the extra influence of the residual stress forming in peeling on the original residual stress in surface, the abrasive particle size would not be too small and the load impressed would not be too large. Some experimental researches on residual stress in surface of silicon nitride ceramic balls were made. The surface of silicon nitride ceramic balls presented residual compressive stress after sintering and the influence of the ball size on the residual stress is feeble. It is expected that the size of ball blank is same for achieving the same residual compressive stress in surface on balls after final machining. In lapping process, the surface of silicon nitride ceramic balls presented residual tensile stress, the larger the load which is impressed on single ball, the larger the amplitude of residual tensile stress is; the smaller the abrasive particle, the stronger the trend of plastic deformation is and the larger the amplitude of residual tensile stress is.

Break-up Process of Perturbed Molten Metal Jet and Preparation of Lead-Free Solder Balls

Solder balls, which are used in advanced electronics packages such as BGA (Ball Grid Array) and CSP (Chip Scale Package) to substitute the leads and realize the electrical and mechanical connections between substrate and chip,have severe specifications in diameter tolerance, roundness and surface quality, and therefore challenge the traditional technologies for fabrication of metallic particles and powders. The present work made a survey of perturbed molten metal jet break-up process, observed the formation and growth of capillary wave of tin-lead melt jet by way of rapid solidification, and on the basis of the above research, successfully obtained tin-lead eutectic and Sn-4.0Ag-0.5Cu lead free solder balls with tight distribution and good sphericity of particles through optimization of processing parameters, forming a solid base for cost effectively producing solder balls.

Dye-sensitized solid-state solar cells fabricated by screen-printed TiO_2 thin film with addition of polystyrene balls

The screen-printed nanoporous TiO2 thin film was employed to fabricate dye-sensitized solid-state solar cells using CuI as hole-transport materials. The solar cell based on nanoporous TiO2 thin film with large pores formed by the addition of polystyrene balls with diameter of 200 nm to the TiO2 paste exhibits photovoltaic performance enhancement, which is attributed to the good contact of CuI with surface of dye-sensitized thin film due to easy penetration of CuI in the film with large pores.

Enhanced removal of ultra fi ne particles from kerosene combustion using a dielectric barrier discharge reactor packed with porous alumina balls

Ultrafine particles(UFPs)are harmful to human beings,and their effective removal from the environment is an urgent necessity.In this study,a dielectric barrier discharge(DBD)reactor packed with porous alumina(PA)balls driven by a pulse power supply was developed to remove the UFPs(ranging from 20 to 100 nm)from the exhaust gases of kerosene combustion.Five types of DBD reactors were established to evaluate the effect of plasma catalysis on the removal efficiency of UFPs.The influences of gasflow rate,peak voltage and pulse frequency of different reactors on UFPs removal were investigated.It was found that a high total UFP removal of 91.4%can be achieved in the DBD reactor entirely packed with PA balls.The results can be attributed to the enhanced charge effect of the UFPs with PA balls in the discharge space.The UFP removals by diffusion deposition and electrostatic attraction were further calculated,indicating that particle charging is vital to achieve high removal efficiency for UFPs.

Are Black Holes 4-D Spatial Balls Filled with Black Body Radiation? Generalization of the Stefan-Boltzmann Law and Young-Laplace Relation for Spatial Radiative Transfers

This is the first paper in a two part series on black holes. In this work, we concern ourselves with the event horizon. A second follow-up paper will deal with its internal structure. We hypothesize that black holes are 4-dimensional spatial, steady state, self-contained spheres filled with black-body radiation. As such, the event horizon marks the boundary between two adjacent spaces, 4-D and 3-D, and there, we consider the radiative transfers involving black- body photons. We generalize the Stefan-Boltzmann law assuming that photons can transition between different dimensional spaces, and we can show how for a 3-D/4-D interface, one can only have zero, or net positive, transfer of radiative energy into the black hole. We find that we can predict the temperature just inside the event horizon, on the 4-D side, given the mass, or radius, of the black hole. For an isolated black hole with no radiative heat inflow, we will assume that the temperature, on the outside, is the CMB temperature, T2 = 2.725 K. We take into account the full complement of radiative energy, which for a black body will consist of internal energy density, radiative pressure, and entropy density. It is specifically the entropy density which is responsible for the heat flowing in. We also generalize the Young- Laplace equation for a 4-D/3-D interface. We derive an expression for the surface tension, and prove that it is necessarily positive, and finite, for a 4-D/3-D membrane. This is important as it will lead to an inherently positively curved object, which a black hole is. With this surface tension, we can determine the work needed to expand the black hole. We give two formulations, one involving the surface tension directly, and the other involving the coefficient of surface tension. Because two surfaces are expanding, the 4-D and the 3-D surfaces, there are two radiative contributions to the work done, one positive, which assists expansion. The other is negative, which will resist an increase in volume. The 4-D side promotes expansion whereas the 3-D side hinders it. At the surface itself, we also have gravity, which is the major contribution to the finite surface tension in almost all situations, which we calculate in the second paper. The surface tension depends not only on the size, or mass, of the black hole, but also on the outside surface temperature, quantities which are accessible observationally. Outside surface temperature will also determine inflow. Finally, we develop a “waterfall model” for a black hole, based on what happens at the event horizon. There we find a sharp discontinuity in temperature upon entering the event horizon, from the 3-D side. This is due to the increased surface area in 4-D space, AR(4) = 2π2R3, versus the 3-D surface area, AR(3) = 4πR2. This leads to much reduced radiative pressures, internal energy densities, and total energy densities just inside the event horizon. All quantities are explicitly calculated in terms of the outside surface temperature, and size of a black hole. Any net radiative heat inflow into the black hole, if it is non-zero, is restricted by the condition that, 0cdQ/dt FR(3), where, FR(3), is the 3-D radiative force applied to the event horizon, pushing it in. We argue throughout this paper that a 3-D/3-D interface would not have the same desirable characteristics as a 4-D/3-D interface. This includes allowing for only zero or net positive heat inflow into the black hole, an inherently positive finite radiative surface tension, much reduced temperatures just inside the event horizon, and limits on inflow.

Drag Coefficients of Golf Balls

Drag across a golf ball can affect distance traveled when hitting a ball. An average golf ball will have a drag coefficient of, 0.24 CD ReD 35 m/s. This research found that a significantly deeper dimple pattern will greatly affect the boundary layer, thus changing the drag coefficient and boundary layer.

Preliminary Study on the Seizure Trend of a MOM-THP with Self-directed Balls

This work continues the approach of one of our topics relating to a MOM-THP （metal on metal-total hip prostheses） with self-directed movement balls. Experiments revealed a certain seizure in some strain conditions. Laboratory trials for balls/plane Hertzian contacts have been restarted in order to determine seizure behaviour depending on the roughness of the flat area. The trials have been carried out in BSF （body simulated fluid） lubrication conditions, much closer to the real operating conditions up against the initial tests with distilled water. Seizure burdens to different loadings and contact surfaces roughness influence over the seizure burden have been determined. Even though the minimum value of the wear must be the same with the minimum value of the surfaces roughness, given the experimental conditions, it came out from the trials results on wear that the lowest level of wear is acquired at a certain value of roughness, not at the lowest level of roughness.

Research on Devices for Dividing Balls with Fluid

The methods of dividing balls equally among ball bearings to install the bearing retainer is briefly introduced in this paper, and the insufficiency of traditional methods is pointed out. A novel kind of non-contact type of dividing ball method is proposed, according to the principle theory.